Abstract. In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field satisfies a monotonicity assumption: we prove the uniqueness of a solution for first order systems modeling crowd motion with hard congestion effects, introduced recently by Maury et al. The monotonicity of the velocity field implies that the 2−Wasserstein distance along two solutions is λ-contractive, which in particular implies uniqueness. In the case of diffusive models, we prove the uniqueness of a solution passing through the dual equation, where we use some well-known parabolic estimates to conclude an L 1 −contraction property. In this case, by the regularization effect of the non-degenerate diffusion, the result follows even if the given velocity field is only L ∞ as in the standard FokkerPlanck equation.